Approximate solutions to the one-phase Stefan problem with non-linear temperature-dependent thermal conductivity
Abstract
In this chapter we consider different approximations for the one-dimensional one-phase Stefan problem corresponding to the fusion process of a semi-infinite material with a temperature boundary condition at the fixed face and non-linear temperature-dependent thermal conductivity. The knowledge of the exact solution of this problem, allows to compare it directly with the approximate solutions obtained by applying the heat balance integral method, an alternative form to it and the refined balance integral method, assuming a quadratic temperature profile in space. In all cases, the analysis is carried out in a dimensionless way by the Stefan number (Ste) parameter.
Cite
@article{arxiv.1906.08601,
title = {Approximate solutions to the one-phase Stefan problem with non-linear temperature-dependent thermal conductivity},
author = {Julieta Bollati and María F. Natale and José A. Semitiel and Domingo A. Tarzia},
journal= {arXiv preprint arXiv:1906.08601},
year = {2019}
}
Comments
23 pages, 7 figures. arXiv admin note: substantial text overlap with arXiv:1808.02842, arXiv:1810.06370